Advanced Statistics: Pride Forex
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.189 | ||||
| SD | 0.403 | ||||
| Sharpe ratio (Glass type estimate) | 0.470 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.463 | ||||
| df | 54.000 | ||||
| t | 1.006 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.452 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.387 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.456 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.383 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.684 | ||||
| Upside Potential Ratio | 1.539 | ||||
| Upside part of mean | 0.426 | ||||
| Downside part of mean | -0.236 | ||||
| Upside SD | 0.293 | ||||
| Downside SD | 0.277 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.351 | ||||
| Mean of criterion | 0.189 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.403 | ||||
| Covariance | -0.002 | ||||
| r | -0.021 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | 0.201 | ||||
| Mean Square Error | 0.165 | ||||
| DF error | 53.000 | ||||
| t(b) | -0.154 | ||||
| p(b) | 0.561 | ||||
| t(a) | 0.981 | ||||
| p(a) | 0.166 | ||||
| Lowerbound of 95% confidence interval for beta | -0.477 | ||||
| Upperbound of 95% confidence interval for beta | 0.409 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.210 | ||||
| Upperbound of 95% confidence interval for alpha | 0.613 | ||||
| Treynor index (mean / b) | -5.574 | ||||
| Jensen alpha (a) | 0.201 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.098 | ||||
| SD | 0.447 | ||||
| Sharpe ratio (Glass type estimate) | 0.221 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.217 | ||||
| df | 54.000 | ||||
| t | 0.472 | ||||
| p | 0.319 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.697 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.136 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.699 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.272 | ||||
| Upside Potential Ratio | 1.074 | ||||
| Upside part of mean | 0.388 | ||||
| Downside part of mean | -0.290 | ||||
| Upside SD | 0.257 | ||||
| Downside SD | 0.361 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 55.000 | ||||
| Mean of predictor | 0.316 | ||||
| Mean of criterion | 0.098 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.447 | ||||
| Covariance | 0.009 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 0.155 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.202 | ||||
| DF error | 53.000 | ||||
| t(b) | 0.617 | ||||
| p(b) | 0.270 | ||||
| t(a) | 0.220 | ||||
| p(a) | 0.413 | ||||
| Lowerbound of 95% confidence interval for beta | -0.349 | ||||
| Upperbound of 95% confidence interval for beta | 0.660 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.401 | ||||
| Upperbound of 95% confidence interval for alpha | 0.499 | ||||
| Treynor index (mean / b) | 0.634 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.184 | ||||
| Expected Shortfall on VaR | 0.226 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.116 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 55.000 | ||||
| Minimum | 0.513 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.047 | ||||
| Maximum | 1.396 | ||||
| Mean of quarter 1 | 0.932 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.134 | ||||
| Inter Quartile Range | 0.047 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.055 | ||||
| Mean of outliers low | 0.696 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 1.301 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.030 | ||||
| VaR(95%) (regression method) | 0.131 | ||||
| Expected Shortfall (regression method) | 0.367 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.323 | ||||
| Quartile 1 | 0.370 | ||||
| Median | 0.416 | ||||
| Quartile 3 | 0.462 | ||||
| Maximum | 0.508 | ||||
| Mean of quarter 1 | 0.323 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.508 | ||||
| Inter Quartile Range | 0.092 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.201 | ||||
| Compounded annual return (geometric extrapolation) | 0.153 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.301 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.301 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.677 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.236 | ||||
| SD | 0.517 | ||||
| Sharpe ratio (Glass type estimate) | 0.456 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.455 | ||||
| df | 1214.000 | ||||
| t | 0.981 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.455 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.366 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.455 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.366 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.670 | ||||
| Upside Potential Ratio | 4.663 | ||||
| Upside part of mean | 1.639 | ||||
| Downside part of mean | -1.403 | ||||
| Upside SD | 0.379 | ||||
| Downside SD | 0.352 | ||||
| N nonnegative terms | 268.000 | ||||
| N negative terms | 947.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1215.000 | ||||
| Mean of predictor | 0.376 | ||||
| Mean of criterion | 0.236 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.517 | ||||
| Covariance | 0.012 | ||||
| r | 0.070 | ||||
| b (slope, estimate of beta) | 0.112 | ||||
| a (intercept, estimate of alpha) | 0.194 | ||||
| Mean Square Error | 0.266 | ||||
| DF error | 1213.000 | ||||
| t(b) | 2.460 | ||||
| p(b) | 0.455 | ||||
| t(a) | 0.805 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | 0.023 | ||||
| Upperbound of 95% confidence interval for beta | 0.202 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.278 | ||||
| Upperbound of 95% confidence interval for alpha | 0.665 | ||||
| Treynor index (mean / b) | 2.101 | ||||
| Jensen alpha (a) | 0.194 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.097 | ||||
| SD | 0.536 | ||||
| Sharpe ratio (Glass type estimate) | 0.181 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.181 | ||||
| df | 1214.000 | ||||
| t | 0.389 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.730 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.091 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.730 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.091 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.239 | ||||
| Upside Potential Ratio | 3.885 | ||||
| Upside part of mean | 1.574 | ||||
| Downside part of mean | -1.477 | ||||
| Upside SD | 0.350 | ||||
| Downside SD | 0.405 | ||||
| N nonnegative terms | 268.000 | ||||
| N negative terms | 947.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1215.000 | ||||
| Mean of predictor | 0.322 | ||||
| Mean of criterion | 0.097 | ||||
| SD of predictor | 0.330 | ||||
| SD of criterion | 0.536 | ||||
| Covariance | 0.022 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.199 | ||||
| a (intercept, estimate of alpha) | 0.033 | ||||
| Mean Square Error | 0.283 | ||||
| DF error | 1213.000 | ||||
| t(b) | 4.300 | ||||
| p(b) | 0.422 | ||||
| t(a) | 0.133 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | 0.108 | ||||
| Upperbound of 95% confidence interval for beta | 0.290 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.453 | ||||
| Upperbound of 95% confidence interval for alpha | 0.518 | ||||
| Treynor index (mean / b) | 0.487 | ||||
| Jensen alpha (a) | 0.033 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.066 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1215.000 | ||||
| Minimum | 0.556 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.403 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 221.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.971 | ||||
| Number of outliers high | 270.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.377 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.012 | ||||
| Extreme Value Index (regression method) | 0.208 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 28.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.105 | ||||
| Maximum | 0.581 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.040 | ||||
| Mean of quarter 4 | 0.263 | ||||
| Inter Quartile Range | 0.095 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.107 | ||||
| Mean of outliers high | 0.407 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.322 | ||||
| VaR(95%) (moments method) | 0.250 | ||||
| Expected Shortfall (moments method) | 0.309 | ||||
| Extreme Value Index (regression method) | 0.129 | ||||
| VaR(95%) (regression method) | 0.385 | ||||
| Expected Shortfall (regression method) | 0.610 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.199 | ||||
| Compounded annual return (geometric extrapolation) | 0.151 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.260 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.575 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.305 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.175 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.394 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.095 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.396 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8673021592215858.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -62312320252081563249438871257088.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||